Question

Express the product of (1/5x + 1) and (1/6x + 5/4) as a trinomial in simplest form

Answer 1

$(\frac{1}{5}x+1)(\frac{1}{6}x+\frac{5}{4})$

Use distributive property to remove the parentheses:

$(a+b)(c+d)=ac+ad+bc+bd$$\begin{gathered} =\frac{1}{5}x*\frac{1}{6}x+\frac{1}{5}x*\frac{5}{4}+1*\frac{1}{6}x+1*\frac{5}{4} \\ \\ Multiplication\text{ }of\text{ }fractions: \\ \frac{a}{b}*\frac{c}{d}=\frac{a*c}{b*d} \\ \\ =\frac{1}{30}x^2+\frac{5}{20}x+\frac{1}{6}x+\frac{5}{4} \\ \\ =\frac{1}{30}x^2+\frac{1}{4}x+\frac{1}{6}x+\frac{5}{4} \\ \\ Addition\text{ }of\text{ }fractions: \\ \frac{a}{b}+\frac{c}{d}=\frac{ad+bc}{bd} \\ \\ =\frac{1}{30}x^2+(\frac{6x+4x}{24})+\frac{5}{4} \\ \\ =\frac{1}{30}x^2+\frac{10}{24}x+\frac{5}{4} \\ \\ Simplify: \\ =\frac{1}{30}x^2+\frac{5}{12}x+\frac{5}{4} \end{gathered}$Then, the product in the simplest form is:$\frac{1}{30}x^2+\frac{5}{12}x+\frac{5}{4}$